You do realize that 'real cheddar' is dyed orange, don't you? "White Cheddar" is undyed cheese.
Orange cheese originated in America.
Both right and wrong.
That garish orange tint that you see in cheap cheese, yes, that is dye.
I make cheese (Cheshire cheese mostly) and what cheddar I do make is naturally yellow in color. It is a case of what kind of milk you are using.
The milk from my Jerseys has a yellow tint and cheese as a result is a nice golden hue.